A heavy freight train has a mass of 14000 metric tons. If the locomotive can pull with a force of 645000 N, how long does it take to increase it's speed from 0 to 69.8 km/h?
To determine the time it takes for the train to increase its speed from 0 to 69.8 km/h, we need to use Newton's second law of motion:
Force = mass * acceleration
In this case, the force is the tractive force exerted by the locomotive, which is 645,000 N. The mass of the train is given as 14,000 metric tons. However, we need to convert this mass to kilograms, as the SI unit for mass is kilogram (kg).
1 metric ton = 1000 kg
Therefore, the mass of the train is:
mass = 14,000 metric tons * 1000 kg/metric ton = 14,000,000 kg
Next, we need to calculate the acceleration of the train. Using the equation of motion:
v = u + at
Where:
v = final velocity (69.8 km/h)
u = initial velocity (0)
a = acceleration
t = time
Given that the initial velocity is 0, the equation simplifies to:
v = at
Converting the velocity from km/h to m/s:
69.8 km/h * (1000 m/km) / (3600 s/h) ≈ 19.4 m/s
Therefore, the equation becomes:
19.4 m/s = a * t
We can rearrange the equation to solve for the acceleration:
a = 19.4 m/s / t
Now we substitute the values of force and mass into Newton's second law:
Force = mass * acceleration
645,000 N = 14,000,000 kg * (19.4 m/s) / t
To isolate the variable t, we divide both sides of the equation by 14,000,000 kg and multiply by t:
(645,000 N * t) / 14,000,000 kg = 19.4 m/s
Finally, to solve for t, we rearrange the equation:
t = (19.4 m/s * 14,000,000 kg) / 645,000 N
Calculating this expression:
t ≈ 420.3 seconds
Therefore, it takes approximately 420.3 seconds for the heavy freight train to increase its speed from 0 to 69.8 km/h.